Lecture #8 OUTLINE Generation and recombination Excess carrier concentrations Minority carrier lifetime Read: Section 3.3

Generation and Recombination Generation and recombination processes act to change the carrier concentrations, and thereby indirectly affect current flow EE130 Lecture 8, Slide 2

Generation Processes Band-to-Band R-G Center Impact Ionization EE130 Lecture 8, Slide 3

Recombination Processes Direct R-G Center Auger Recombination in Si is primarily via R-G centers EE130 Lecture 8, Slide 4

Direct vs. Indirect Band Gap Materials E-k Diagrams Little change in momentum is required for recombination momentum is conserved by photon emission Large change in momentum is required for recombination momentum is conserved by phonon + photon emission EE130 Lecture 8, Slide 5

Excess Carrier Concentrations equilibrium values Charge neutrality condition: EE130 Lecture 8, Slide 6

“Low-Level Injection” Often the disturbance from equilibrium is small, such that the majority-carrier concentration is not affected significantly: For an n-type material: For a p-type material: However, the minority carrier concentration can be significantly affected EE130 Lecture 8, Slide 7

Indirect Recombination Rate Suppose excess carriers are introduced into an n-type Si sample (e.g. by temporarily shining light onto it) at time t = 0. How does p vary with time t > 0? Consider the rate of hole recombination via traps: Under low-level injection conditions, the hole generation rate is not significantly affected: EE130 Lecture 8, Slide 8

The net rate of change in p is therefore EE130 Lecture 8, Slide 9

Relaxation to Equilibrium State Consider a semiconductor with no current flow in which thermal equilibrium is disturbed by the sudden creation of excess holes and electrons. The system will relax back to the equilibrium state via the R-G mechanism: for electrons in p-type material for holes in n-type material EE130 Lecture 8, Slide 10

Minority Carrier (Recombination) Lifetime The minority carrier lifetime  is the average time an excess minority carrier “survives” in a sea of majority carriers  ranges from 1 ns to 1 ms in Si and depends on the density of metallic impurities (contaminants) such as Au and Pt, and the density of crystalline defects. These deep traps capture electrons or holes to facilitate recombination and are called recombination-generation centers. EE130 Lecture 8, Slide 11

Example: Photoconductor Consider a sample of Si doped with 1016 cm-3 boron, with recombination lifetime 1 s. It is exposed continuously to light, such that electron-hole pairs are generated throughout the sample at the rate of 1020 per cm3 per second, i.e. the generation rate GL = 1020/cm3/s What are p0 and n0 ? What are n and p ? (Note: In steady-state, generation rate equals recombination rate.) EE130 Lecture 8, Slide 12

Note: The np product can be very different from ni2. What are p and n ? What is the np product ? Note: The np product can be very different from ni2. EE130 Lecture 8, Slide 13

Net Recombination Rate (General Case) For arbitrary injection levels and both carrier types in a non-degenerate semiconductor, the net rate of carrier recombination is: EE130 Lecture 8, Slide 14

Summary Generation and recombination (R-G) processes affect carrier concentrations as a function of time, and thereby current flow Generation rate is enhanced by deep (near midgap) states associated with defects or impurities, and also by high electric field Recombination in Si is primarily via R-G centers The characteristic constant for (indirect) R-G is the minority carrier lifetime: Generally, the net recombination rate is proportional to EE130 Lecture 8, Slide 15